And another games theory puzzle?!
Question: This one is about a truel, which is like a duel, but fought between three people. There's three guys again, let's call them Arthur, Dan and James. There's been some mutual offence caused between the three of them, yadda-ya, doesn't matter, so they decide to have a truel.
Now Arthur is a pretty poor shot - he can only hit a target one time out of three. Dan is better, he averages 2 out of three, but James is the best. James is pretty much guaranteed to hit his target.
So the way they decide to do it is this. Arthur will take the first shot. If he misses, Dan gets the next shot. If Arthur hits Dan, James gets the next shot. After Dan shoots, James gets his shot, if he's still alive. It keeps going around in that order till there's only one man standing.
You can take "hit" to mean the same as "kill" for this puzzle. The question is, what should Arthur do with his first shot?
Answers: This one is about a truel, which is like a duel, but fought between three people. There's three guys again, let's call them Arthur, Dan and James. There's been some mutual offence caused between the three of them, yadda-ya, doesn't matter, so they decide to have a truel.
Now Arthur is a pretty poor shot - he can only hit a target one time out of three. Dan is better, he averages 2 out of three, but James is the best. James is pretty much guaranteed to hit his target.
So the way they decide to do it is this. Arthur will take the first shot. If he misses, Dan gets the next shot. If Arthur hits Dan, James gets the next shot. After Dan shoots, James gets his shot, if he's still alive. It keeps going around in that order till there's only one man standing.
You can take "hit" to mean the same as "kill" for this puzzle. The question is, what should Arthur do with his first shot?
Fire it into the ground.
Arthur has a better chance of surviving by making Dan & James shoot at each other. Once one of them dies, Arthur can take a shot at the survivor.
More info: OK, I did the math.
If Arthur hits Dan with his first shot, James kills Arthur. Arthur's chances = 0%
If Arthur hits James with his first shot, then Dan shoots at Arthur, Arthur (if he survives) shoots back at Dan ... it's a converging series, Arthur's chance of winning comes to 12.5%.
If Arthur misses them both, then either James kills Dan and Arthur has a one-third chance of killing James, or Dan kills James and duels Arthur again (only this time Arthur gets to shoot first). Arthurs total chance improves to just over 36.1%
So Arthurs best chance is if he doesn't kill anyone on his first shot. He should just shoot into the ground.
If you want more detailed math, email me.
And the last man standing is the referee/second.
Arthur should hit James. Since James is will hit every time, Arthur can die right away if James chooses to hit Arthur. Dan would only hit 2/3 of the time, so Arthur has a much better chance of living if he tries to hit James first. Then Dan should hit James (if Arthur misses.) because Dan has the same chance of dying as Arthur, and he would want to prevent that. Then Arthur should hit Dan to make sure he is the last one standing (and because Dan is the only one left.). Then if he misses, Dan would try to hit James (and he has a high chance of hitting). It would keep going until either Dan or Arthur has been hit.
Arthur should miss, then Dan will shoot at James (because he thinks that James will shoot him if he is still alive). If Dan misses James, then James will shoot Dan because he is the better shot. This gives Arthur the next shot; he has already missed once so now he has a 50/50 chance of killing James. If Dan shoots James, then it is Arthurs' shot again and he has a 50/50 chance of killing Dan. If Arthur misses, then Dan has a 50/50 chance of killing Arthur. If Arthur kills one of the guys with his first shot he is in trouble; If he shoots James, then Dan has a 2/3 chance of killing him with the next shot and if he kills Dan with his first shot, James will not miss. And Arthur has only 2 misses leftTherefore, by missing, Arthur has increased his odds of survival from 33.3% to 50%
im sorry can u repeat that and slower and easier to understand?
Try to hit James?
fire into the air